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In a "dice pool," one considers each die individually, rather than as a collection of components to be summed. As an example, an attack in the HERO System might do 8d6 damage; to resolve it, you'd roll eight six-sided dice and add them up to produce a number between 8 and 48. In a die pool system, you might see how many of the dice showed a 5 or a 6 on the top face, and count those as "successes" toward a benchmark.

Rolling vs. a target number can be used in both die pool systems and otherwise. In HERO, for example, you roll 3d6 and sum them, trying to stay below 11 (or an otherwise modified target). In Deadlands, you use your die pool and select the highest rolled die, comparing it with a target number modified by the difficulty of the task at hand.

In recent usage, a "Dice Pool" system means each die is individually compared to a TN, while a "roll vs target number" mechanic usually means to total all the thrown dice.

In older usage, dice pool simply meant those dice being grabbed to be rolled, and didn't limit it to counting individual dice. This was the case especially for some systems where skill determines number of dice thrown, and they are all totalled, such as the d6 system or L5R, and in the text of some recent editions of L5R and in Houses of the Blooded. Note that EABA and L5R, the dice totalled are usually a subset of the dice in the pool.

Dice pool is almost never used to refer to games where all rolls are made with a specific number and type of dice. Examples of this are 2300AD, MegaTraveller, D&D, and Palladium. For example purposes, 2300AD always uses 3d6 and 1d10; the D10 is used for success, the 3d6 for time, but it's almost never called a dice pool system, even by those who call Star Wars d6 a dice pool system.

The classic "dice pool - count successes" systems are Shadowrun (through 3rd ed) and Vampire 1st Ed - the number of dice are determined by stats and skills, while the TN is set by difficulty. Each game uses a single type of die.

More modern "dice pool - count successes" systems often use a single TN, and difficulty is the number of dice required to succeed in order for the action to succeed. Examples include most of the old StoryTeller system games, and all the newer StoryTeller system games, as well as Burning Wheel and Mouse Guard. Again, a single type of die is used.

Vincent Baker's Dogs in the Vinyard uses a dice pool of multiple types of dice; and does some strange math with them... while I've read it, I don't quite grasp it, other than you pul dice from the pool to be counted individually.

Greg Stoltze's Reign uses a pool of dice by ability, with the number of dice that match each other determining one element of success, and the face showing another element of success.

Simply put, the dice pool is a bit of a squishy word that describes any time you roll a handful of dice instead of a single die to determine the result of an action.

Usually it describes any mechanic where you roll dice and compare against a target number. Since you have more dice rolling, it's less random than mechanics like D&D, and theoretically it makes it much harder for a Zen Swordmaster who's been studying the sword for 50 years to be taken down in a single swing by Cleetus the farmboy (don't laugh, I've seen something like this happen at a gaming table).

In shadowrun, you use 6 sided dice. If your Pistol skill is 5, you roll 5 6-sided dice to see if you shoot the bad guy or not. There are also other pools of dice (notably combat, astral, hacking, and control pools) that enable you to add dice to the test.

For example, you are in a very tense situation, and NEED to hit the bad guy. Your Pistol Skill is 5, and you have a Combat Pool of 5. You could then use some (or all) of your Combat Pool dice to try to make a more impossible shot; or since Shadowrun lets you use extra success dice to increase damage, you could take a small gun, use all your pool dice and (if you are lucky) get enough successes to guarantee a deadly wound to the bad guy.

Other examples of mechanics that use dice pools include:
Old World of Darkness, (I believe New World of Darkness, but don't quote me on that), and if anyone else knows of any, I'll happy edit to list them in here.

Dice pools are used either to describe that you have a bunch of dice which will not be added up but scored individually or that you have a flexible reserve of dice that you can apply to certain actions.

Amusingly, both terms have been used in the Shadowrun game. In SR4, the basic mechanic is a dice pool of the first type; you have a certain number of dice (perhaps adjusted by bonuses and penalties), and you roll them against a target number of 5. In SR3, in contrast, certain actions had dice pools of the second sort: combat pool, for instance, was a flexible reserve of dice that you could use to assist in combat actions, so you could switch between, say, more offensive and more defensive approaches (by applying those dice to one or the other).